\documentclass[11pt]{ctexart}  
\usepackage[top=2cm, bottom=2cm, left=2cm, right=2cm]{geometry}  
\usepackage{algorithm}  
\usepackage{algorithmicx}  
\usepackage{algpseudocode}  
\usepackage{amsmath}  

\floatname{algorithm}{算法}  
\renewcommand{\algorithmicrequire}{\textbf{输入:}}  
\renewcommand{\algorithmicensure}{\textbf{输出:}}  

\begin{document}  
	$$
		\begin{array}{cc}
		t = \hat{\beta} / SE(\hat{\beta}) 
		\\
		\\ \hat{\beta} = \frac {\sum{x_i y_i}} {\sum{x_i^2}} 
		\\
		\\ SE(\hat{\beta}) = \sqrt{\frac {\sum{(y_i - x_i \hat{\beta})^2}} {(n-1) \sum{x_i^2}}}
		\\
		\\
			t = {\frac {\sum{x_i y_i}} {\sum{x_i^2}}}
			{\sqrt{\frac {(n-1) \sum{x_i^2}} {\sum{(y_i - x_i \hat{\beta})^2}}}}
			\\
			\\
		=	\frac {\sqrt{n-1} \sum{x_i y_i}}
			{\sqrt{\sum{x_i^2} \sum{(y_i - x_i \hat{\beta})^2}}}
			\\
			\\
		=	\frac {\sqrt{n-1} \sum{x_i y_i}}
			{\sqrt{\sum{x_i^2} \sum{(y_i^2 - 2 \hat{\beta} x_i y_i  + x_i^2 \hat{\beta}^2)}}}
			\\
			\\
		=	\frac {\sqrt{n-1} \sum{x_i y_i}}
			{\sqrt{\sum{x_i^2} \sum{y_i^2} - 
					\sum{x_i^2} \hat{\beta} (2 \sum{x_i y_i} - \hat{\beta} \sum{x_i^2})}}
			\\
			\\
		=	\frac {\sqrt{n-1} \sum{x_i y_i}}
			{\sqrt{\sum{x_i^2} \sum{y_i^2} - 
					\sum{x_i y_i} (2 \sum{x_i y_i} - \sum{x_i y_i})}}
			\\
			\\
			t = \frac {\sqrt{n-1} \sum{x_i y_i}} 
			{\sqrt{\sum{x_i^2} \sum{y_i^2} - (\sum{x_i y_i})^2 }}
		\end{array}
	$$
	
\end{document}